Research on dynamic characteristics of arc under electrode relative motion

The relative motion of the electrodes is a typical feature of sliding electrical contact systems.The system fault caused by the arc is the key problem that restricts the service life of the sliding electrical contact system.In this paper,an arcing experimental platform that can accurately control the relative speed and distance of electrodes is built,and the influence of different electrode speeds and electrode distances on arc motion characteristics is explored.It is found that there are three different modes of arc root motion:single arc root motion mode,single and double arc roots alternating motion mode,and multiple arc roots motion mode.The physical process and influence mechanism of different arc root motion modes are further studied,and the corresponding relationship between arc root motion modes and electrode speed is revealed.In addition,to further explore the distribution characteristics of arc temperature and its influencing factors,an arc magnetohydrodynamic model under the relative motion of electrodes is established,and the variation law of arc temperature under the effect of different electrode speeds and electrode distances is summarized.Finally,the influence mechanism of electrode speed and electrode distance on arc temperature,arc root distance,and arc root speed is clarified.The research results enrich the research system of arc dynamic characteristics in the field of sliding electrical contact,and provide theoretical support for restraining arc erosion and improving the service life of the sliding electrical contact system.

Algebraic Structure of the Dynamical Equations of Holonomic Mechanical System in Relative Motion

Aim To study an algebraic of the dynamical equations of holonomic mechanical systems in relative motion. Methods The equations of motion were presented in a contravariant algebraic form and an algebraic product was determined. Results and Conclusion The equations a Lie algebraic structure if any nonpotential generalized force doesn't exist while while the equations possess a Lie-admissible algebraic structure if nonpotential generalized forces exist .

Lie Symmetries and Conserved Quantities of Systems of Relative Motion Dynamics

Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equaiton of the Lie symmetries for the dynamical equationS of relative motion is established.The structure quation and the form conserved quantities are obtained. An example iD illustrate the application of the result is given.

Conformal invariance and conserved quantities of dynamical system of relative motion

This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.

Special Lie symmetry and Hojman conserved quantity of Appell equations in a dynamical system of relative motion

Special Lie symmetry and the Hojman conserved quantity for Appell equations in a dynamical system of relative motion are investigated. The definition and the criterion of the special Lie symmetry of Appell equations in a dynamical system of relative motion under infinitesimal group transformation are presented. The expression of the equation for the special Lie symmetry of Appell equations and the Hojman conserved quantity, deduced directly from the special Lie symmetry in a dynamical system of relative motion, are obtained. An example is given to illustrate the application of the results.

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion

Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are studied.The definition and criterion of the Mei symmetry of Appell equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups are given.The structural equation of Mei symmetry of Appell equations and the expression of Mei conserved quantity deduced directly from Mei symmetry for a variable mass holonomic system of relative motion are gained.Finally,an example is given to illustrate the application of the results.

Integrating Factors and Conservation Theorems of Nonholonomic Dynamical System of Relative Motion

The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integrating factors is given, and the necessary conditions for the existence of the conserved quantities are studied in detail. Then, the conservation theorem and its inverse of system are established. Finally, an example is given to illustrate the application of the result.

Poisson theory and integration method for a dynamical system of relative motion

This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if （2n-1） first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.

Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints

Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.

Lie symmetry and Hojman conserved quantity of a Nielsen equation in a dynamical system of relative motion with Chetaev-type nonholonomic constraint

The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.

Relative energy zero ratio-based approach for identifying pulse-like ground motions

Pulse-like ground motions are capable of inflicting significant damage to structures. Efficient classification of pulse-like ground motion is of great importance when performing the seismic assessment in near-fault regions. In this study, a new method for identifying the velocity pulses is proposed, based on different trends of two parameters: the short-time energy and the short-time zero crossing rate of a ground motion record. A new pulse indicator, the relative energy zero ratio(REZR), is defined to qualitatively identify pulse-like features. The threshold for pulse-like ground motions is derived and compared with two other identification methods through statistical analysis. The proposed procedure not only shows good accuracy and efficiency when identifying pulse-like ground motions but also exhibits good performance for classifying records with high-frequency noise and discontinuous pulses. The REZR method does not require a waveform formula to express and fit the potential velocity pulses;it is a purely signal-based classification method. Finally, the proposed procedure is used to evaluate the contribution of pulse-like motions to the total input energy of a seismic record, which dramatically increases the seismic damage potential.

Perturbation to Symmetries and Adiabatic Invariants of Nonholonomic Dynamical System of Relative Motion

Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic dynamical system of relative motion are studied. The perturbation to symmetries for the nonholonomic dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.

Noether Symmetry and Noether Conserved Quantity of Nielsen Equation for Dynamical Systems of Relative Motion

Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.

Integrated modeling of spacecraft relative motion dynamics using dual quaternion

To realize high accurate control of relative position and attitude between two spacecrafts, the coupling between position and attitude must be fully considered and a more precise model should be established. This paper breaks the traditional divide and conquer idea, and uses a mathematical tool, namely dual quaternion to establish the integrated 6 degree-of-freedom(6-DOF) model of relative position and attitude, which describes the coupled relative motion in a compact and efficient form and needs less information of the target. Considering the complex operation rules and the unclarity of the current relative motion model in dual quaternion, necessary mathematical foundations are given at first, followed by clear and detailed modeling process and analysis. Finally a generalized proportion-derivative(PD) controller law is designed. The simulation results show that based on the integrated model established by dual quaternion, this control law can achieve a high control accuracy of relative motion.

Mei symmetry and Mei conserved quantity of the Appell equation in a dynamical system of relative motion with non-Chetaev nonholonomic constraints

The Mei symmetry and the Mei conserved quantity of Appell equations in a dynamical system of relative motion with non-Chetaev nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and the criterion of the Mei symmetry,and the expression of the Mei conserved quantity deduced directly from the Mei symmetry for the system are obtained.An example is given to illustrate the application of the results.

Re-Discussion on Motion of Shanghai VLBI Station Relative to Eurasian Plate From VLBI

By using the results of changing rate of the baseline lengths from Shanghai VLBI station to 13 international VLBI stations, respectively, the vertical and horizontal velocities of Shanghai VLBI station are re estimated by means of the Least Square Fit method based on the international VLBI station velocities of ITRF96, and the Euler vectors of Eurasian tectonic plate of Sillard et al (1998). The results are such the vertical velocity: -1 86±0 84 mm/yr, horizontal velocity and its local azimuth: 14 24±0 97 mm/yr, E -12° 49±2° 98 S. If the NNR NUVEL 1A model is used instead of the Euler vectors of Sillard et al., the corresponding results are such -1 86±0 84 mm/yr, 10 56±0 96 mm/yr, E -16° 07±4° 06 S. In addition, the corresponding results for the Urumqi VLBI station are also estimated.

Time-Domain Analysis of the Relative Motions Between Side-by-Side FLNG and LNGC Under Oblique Waves

Strong hydrodynamic interactions during the side-by-side offloading operation between floating liquefied natural gas(FLNG) and liquefied natural gas carrier(LNGC) can induce high risks of collision. The weather vane effect of a single-point mooring system normally results in the satisfactory hydrodynamic performance of the side-by-side configuration in head seas. Nevertheless, the changes in wave directions in real sea conditions can significantly influence the relative motions. This article studies the relative motions of the side-by-side system by using the theoretical analysis method and the numerical calculation method. Based on the three-dimensional potential theory modified by artificial damping-lid method, the frequency-domain hydrodynamic coefficients can be improved to calculate the retardation functions for the multi-body problem. An in-house code is then developed to perform the time-domain simulation of two vessels, through which the relative motions are subsequently obtained. A range of oblique waves are chosen for the extensive calculation of relative motions between the two vessels, which are further analyzed in terms of the phase shift of motion responses induced by specific resonant wave patterns. Investigation results show that wave directions have a significant influence on the relative sway, roll, and yaw motions. Under the circumstance that the absolute phase shift between the roll motions of two vessels approaches 180°, stronger relative motions are induced when LNGC is on the weather side.Moreover, the gap water resonances at high frequencies tend to cause the dangerous opposed oscillation of two vessels in the sway and yaw modes, whereas FLNG reduces the gap water resonances and relative motions when located on the weather side.

Lie-Form Invariance of the Nonholonomic System of Relative Motion in Event Space

In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative motion in event space is given. Secondly, the Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. An example is given to illustrate the application of the results.

How are multiple satellites seen from the ground? Relative apparent motion and formation stabilization

This paper answers how multiple satellites are seen from the ground. This question is inspired by space-advertising, a public exhibition in the night sky using a dot matrix of satellites that are bright enough to be seen by the naked eye. Thus, it is important for space advertisement that the specific dot matrix is seen. Moreover, the stability of the dot matrix during a visible span is very valuable. To stabilize the dot matrix, this study formulates an apparent position of a dot from a representative dot seen from the ground. The formulation, linear functions of a set of relative orbital elements, reveals the appearance of the dot matrix. The proposed relative variable in the formulation drives the instability of the dot matrix, thereby revealing an initial stable configuration of deputies from a chief. The arbitrary dot matrix designed using the configuration is stable even at low elevations without orbital control during the visible span.